Potential energy

  • #1
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Homework Statement


The net force on the mass is the central force F(r) = -k(r-a). Find the potential energy U(r).
a is the spring of natural length and k is spring constant k.

Homework Equations


-dU/dx = F(x)

The Attempt at a Solution


[tex]F(r) = - \frac{ dU }{ dr } implies -k(r-a) = - \frac{ dU }{ dr }[/tex]
So I did this and then integrating both sides I got
[tex]\frac{ kr^2 }{ 2} - kar = U(r)[/tex] but this doesn't make much sense when I graph it out, as it gives me a parabola, and I would be expecting a asymptotic type function?
 

Answers and Replies

  • #2
130
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Well think about what happens when r > a and r < a. Both states have potential energy and would therefore be parabolic with the vertex at r = a

P. S. I can't see your pics because I'm on my phone
 
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Likes oldspice1212
  • #3
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I didn't upload any pics, was just making sure, and yes that makes sense, thank you :)
 
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Likes Brian T
  • #4
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I didn't upload any pics, was just making sure, and yes that makes sense, thank you :)
 
Last edited:
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Likes oldspice1212
  • #5
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Yes, that's must easier to see! Thank you so much!
 

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